Thermodynamic Phase Transition in Magnetic Reconnection

By examining the entropy production in fully kinetic simulations of collisional plasmas, it is shown that the transition from collisional Sweet-Parker reconnection to collisionless Hall reconnection may be viewed as a thermodynamic phase transition. The phase transition occurs when the reconnection electric field satisfies E = ED √me / mi, where me / mi is the electron-to-ion mass ratio and ED is the Dreicer electric field. This condition applies for all mi / me, including mi / me = 1, where the Hall regime vanishes and a direct phase transition from the collisional to the kinetic regime occurs. In the limit me / mi → 0, this condition is equivalent to there being a critical electron temperature Te ≈ mi Ωi2 δ2, where Ωi is the ion cyclotron frequency and δ is the current sheet half-thickness. The heat capacity of the current sheet changes discontinuously across the phase transition, and a critical power law is identified in an effective heat capacity. A model for the time-dependent evolution of an isolated current sheet in the collisional regime is derived.